[2] (4)/(5)times 2(1)/(4)times 2(1)/(3)div 1(1)/(6)

To solve this problem, we need to follow the order of operations (PEMDAS/BODMAS) and perform the multiplication and division from left to right.<br /><br />First, let's convert the mixed fractions to improper fractions:<br /><br />$2\frac{1}{4} = \frac{9}{4}$<br /><br />$2\frac{1}{3} = \frac{7}{3}$<br /><br />$1\frac{1}{6} = \frac{7}{6}$<br /><br />Now, let's rewrite the expression with the improper fractions:<br /><br />$\frac{4}{5} \times \frac{9}{4} \times \frac{7}{3} \div \frac{7}{6}$<br /><br />Next, we can simplify the expression by canceling out common factors:<br /><br />$\frac{4}{5} \times \frac{9}{4} \times \frac{7}{3} \div \frac{7}{6}$<br /><br />Canceling out the common factor of 4:<br /><br />$\frac{1}{5} \times \frac{9}{1} \times \frac{7}{3} \div \frac{7}{6}$<br /><br />Canceling out the common factor of 7:<br /><br />$\frac{1}{5} \times \frac{9}{1} \times \frac{1}{3} \div \frac{1}{6}$<br /><br />Now, let's perform the multiplication:<br /><br />$\frac{1}{5} \times \frac{9}{1} \times \frac{1}{3} = \frac{9}{15}$<br /><br />Finally, let's perform the division:<br /><br />$\frac{9}{15} \div \frac{1}{6} = \frac{9}{15} \times \frac{6}{1} = \frac{54}{15}$<br /><br />Simplifying the fraction:<br /><br />$\frac{54}{15} = \frac{18}{5}$<br /><br />Therefore, the final answer is $\frac{18}{5}$.